Algebra.Com's Answer #831321 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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Probability-and-statistics/1197870:
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document.write( "71% of all voters favor Proposition A and a random sample of 200 voters is taken.
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document.write( "Use the normal approximation to the bonomial to find the following probabilities rounded to 3 decimal places.\r
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document.write( "a. Find the probability that more than 140 of the voters favor Proposition A. Incorrect
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document.write( "b. Find the probability that at most 150 of the voters favor Proposition A. Incorrect
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document.write( "c. Find the probability that between 141 and 149, inclusive, of the voters favor Proposition A.
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document.write( "You have a binomial distribution with large number of trials n = 200 \r\n" );
document.write( "and individual probability of success p = 0.71.\r\n" );
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document.write( "You want to approximate it by the normal distribution.\r\n" );
document.write( "You should use the mean value m = p*n = 0.71*200 = 142 and standard deviation \r\n" );
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document.write( " SD =  =  = 6.417.\r\n" );
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document.write( "Also, you should use the continuity correction factor.\r\n" );
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document.write( "About approximation of the binomial distribution by normal distribution and continuity correction factor \r\n" );
document.write( "see your textbook and/or these Internet sources\r\n" );
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document.write( "https://www.statisticshowto.com/probability-and-statistics/binomial-theorem/normal-approximation-to-the-binomial/\r\n" );
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document.write( "https://online.stat.psu.edu/stat414/lesson/28/28.1\r\n" );
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document.write( "https://stats.libretexts.org/Courses/Las_Positas_College/Math_40%3A_Statistics_and_Probability/06%3A_Continuous_Random_Variables_and_the_Normal_Distribution/6.04%3A_Normal_Approximation_to_the_Binomial_Distribution\r\n" );
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document.write( " For calculations, you may use your calculator (function normcdf), or Excel spreadsheet (function NORMDIST);\r\n" );
document.write( " or online calculator https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
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document.write( "(a) In this case, you should find the area under the normal curve on the right from 140.5\r\n" );
document.write( " (using the correction factor)\r\n" );
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document.write( " P(x > 140) = normcdf(140.5, 9999, 142, 6.417) = 0.592 (rounded).\r\n" );
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document.write( "(b) In this case, you should find the area under the normal curve on the left from 150.5\r\n" );
document.write( " (using the correction factor)\r\n" );
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document.write( " P(x <= 150) = normcdf(-9999, 150.5, 142, 6.417) = 0.907 (rounded). \r\n" );
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document.write( "(c) In this case, you should calculate the area under the normal curve between 140.5 and 149.5\r\n" );
document.write( " (using the correction factor)\r\n" );
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document.write( " P(141 <= x <= 149) = normcdf(140.5, 149.5, 142, 6.417) = 0.471 (rounded). \r\n" );
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document.write( "Solved.\r
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document.write( "If you are a beginner student in learning probability distributions, I advise you to start learning
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document.write( "this kind of computations using the online calculator, to which I referred above.\r
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document.write( "It provides a graphical support, so at each step you do understand what you are doing.
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document.write( "In addition, this graphical support prevents you from making mistakes.\r
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document.write( "When you learn enough this kind of computations, you can switch to your regular calculator,
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document.write( "but even then you may use the online calculator for checking purposes.\r
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